Efficient Algorithms for Semiclassical Quantum Dynamics

Quantum systems of interest in physics and chemistry have many degrees of freedom. The goal of my thesis is to provide numerical methods capable of simulating the dynamics of such systems. I study the Herman-Kluk propagator, which is capable of providing approximate solutions to the time-dependent semiclassical Schrodinger equation in high dimensions. I derive a discretisation scheme and prove rigorous error estimates. Moreover, this scheme as well as other semiclassical methods are of an intrinsically parallel nature. My contributions are the design and implementation of highly efficient algorithms employing state of the art parallelisation and vectorisation techniques.